Question

A solução da equação log9 x + log27 x = 5/3 é:

Answer 1

Vamos là.

log9(x) + log27(x) = 5/3

log(x)/log(9) + log(x)/log(27) = 5/3

log(x)/(2log(3)) + log(x)/(3log(3)) = 5/3

log(x)/log(3) * (1/2 + 1/3) = 5/3

log(x)/log(3) * (5/6) = 5/3

log(x)/log(3) = (5/3)/(5/6)

log(x)/log(3) = 2

log(x) = 2log(3) = log(9)

x = 9